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1. Use limit definition to find f'(2) for the function, f(g;) = 33:2 _ 4:1: + 1. Show detailed work for credit. 2. A coffee shop determines that the daily profit on scones obtained by charging 3 dollars per scone is P(s) = 2052 + 1505 10. The coffee shop currently charges $3.25 per scone. Find P'(3.25), the rate of change of profit when the price is $3.25, and decide whether or not the coffee shop should consider raising or lowering its prices on scones. 3. Use Desmos to graph a cubic polynomial function, f(1:) of your choice and it's derivative, f'(1:) and explain the changes that happened. For example, if :1: = a is where f(1:) has an extreme value (max or min) then what happened to f'(:1:) at :5 = 0.. Explain the following: - If f(:L') is increasing or decreasing in an interval then what happens to f'(g;) in those intervals? - lsf'(a:) above or below the xaxis, and why? Then repeat with the graph a polynomial function, f(1:) of degree 4 and repeat the same exercises. Show your work in full for maximum credit. 4. For the following exercises, the given limit represents the derivative of a function y = f(:l:) at a: = 0.. Find f(:c) and a. . , (1+h)2/31 0 ll 11m hbO h. (2 + h)\" 16 "l Ill13(1) h. . . . . . _ 2 9(1) . 5. Use derivative rules to find the derivative of My) _ 3f\") _ 29(1) _ 5,; f(g;) + 1. Show steps for full credit. J_.:'x_ 6. Find the values of :1: at which the graph off(g;) = 43:2 _ 3;; + 2 has a tangent line parallel to the line y = 2g: + 3. Show detailed work for full credit. 7. Find the equation of a line tangent to the graph of f(:1:) = cote: at :1: = 7r/4. Show all steps to receive full credit. 8. Find the derivative of f(:1:) = 2tm$ 38661:. Show all steps to receive full credit. 9. Find the derivative of the following functions (show all the steps for full credit): i) x) = - ii)f(:1:) = 9321129